213 research outputs found
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Multilayer Networks in a Nutshell
Complex systems are characterized by many interacting units that give rise to
emergent behavior. A particularly advantageous way to study these systems is
through the analysis of the networks that encode the interactions among the
system's constituents. During the last two decades, network science has
provided many insights in natural, social, biological and technological
systems. However, real systems are more often than not interconnected, with
many interdependencies that are not properly captured by single layer networks.
To account for this source of complexity, a more general framework, in which
different networks evolve or interact with each other, is needed. These are
known as multilayer networks. Here we provide an overview of the basic
methodology used to describe multilayer systems as well as of some
representative dynamical processes that take place on top of them. We round off
the review with a summary of several applications in diverse fields of science.Comment: 16 pages and 3 figures. Submitted for publicatio
A rank-3 network representation for single-affiliation systems
Single-affiliation systems are observed across nature and society. Examples
include collaboration, organisational affiliations, and trade-blocs. The study
of such systems is commonly approached through network analysis. Multilayer
networks extend the representation of network analysis to include more
information through increased dimensionality. Thus, they are able to more
accurately represent the systems they are modelling. However, multilayer
networks are often represented by rank-4 adjacency tensors, resulting in a N2M2
solution space. Single-affiliation systems are unable to occupy the full extent
of this space leading to sparse data where it is difficult to attain
statistical confidence through subsequent analysis. To overcome these
limitations, this paper presents a rank-3 tensor representation for
single-affiliation systems. The representations is able to maintain full
information of single-affiliation networks in directionless networks, maintain
near full information in directed networks, reduce the solution space it
resides in (N2M) leading to statistically significant findings, and maintain
the analytical capability of multilayer approaches. This is shown through a
comparison of the rank-3 and rank-4 representations which is performed on two
datasets: the University of Bath departmental journal co-authorship 2000-2017
and an Erdos-Renyi network with random single-affiliation. The results
demonstrate that the structure of the network is maintained through both
representations, while the rank-3 representation provides greater statistical
confidence in node-based measures, and can readily show inter- and
intra-affiliation dynamics.Comment: 17 pages, 11 figure
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201
Towards real-world complexity: an introduction to multiplex networks
Many real-world complex systems are best modeled by multiplex networks of
interacting network layers. The multiplex network study is one of the newest
and hottest themes in the statistical physics of complex networks. Pioneering
studies have proven that the multiplexity has broad impact on the system's
structure and function. In this Colloquium paper, we present an organized
review of the growing body of current literature on multiplex networks by
categorizing existing studies broadly according to the type of layer coupling
in the problem. Major recent advances in the field are surveyed and some
outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure
Mathematical formulation of multilayer networks
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems
A Tensor-Based Formulation of Hetero-functional Graph Theory
Recently, hetero-functional graph theory (HFGT) has developed as a means to
mathematically model the structure of large flexible engineering systems. In
that regard, it intellectually resembles a fusion of network science and
model-based systems engineering. With respect to the former, it relies on
multiple graphs as data structures so as to support matrix-based quantitative
analysis. In the meantime, HFGT explicitly embodies the heterogeneity of
conceptual and ontological constructs found in model-based systems engineering
including system form, system function, and system concept. At their
foundation, these disparate conceptual constructs suggest multi-dimensional
rather than two-dimensional relationships. This paper provides the first
tensor-based treatment of some of the most important parts of hetero-functional
graph theory. In particular, it addresses the "system concept", the
hetero-functional adjacency matrix, and the hetero-functional incidence tensor.
The tensor-based formulation described in this work makes a stronger tie
between HFGT and its ontological foundations in MBSE. Finally, the tensor-based
formulation facilitates an understanding of the relationships between HFGT and
multi-layer networks
The rise and fall of countries in the global value chains
Countries become global leaders by controlling international and domestic transactions connecting geographically dispersed production stages. We model global trade as a multi-layer network and study its power structure by investigating the tendency of eigenvector centrality to concentrate on a small fraction of countries, a phenomenon called localization transition. We show that the market underwent a significant drop in power concentration precisely in 2007 just before the global financial crisis. That year marked an inflection point at which new winners and losers emerged and a remarkable reversal of leading role took place between the two major economies, the US and China. We uncover the hierarchical structure of global trade and the contribution of individual industries to variations in countries’ economic dominance. We also examine the crucial role that domestic trade played in leading China to overtake the US as the world’s dominant trading nation. There is an important lesson that countries can draw on how to turn early signals of upcoming downturns into opportunities for growth. Our study shows that, despite the hardships they inflict, shocks to the economy can also be seen as strategic windows countries can seize to become leading nations and leapfrog other economies in a changing geopolitical landscape
Computation in Complex Networks
Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicin
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